Answer
425.4k+ views
Hint:
In a face centred cubic (fcc) lattice, the atoms of the given substance are located on all 6 sides of the cubic structure as well as on all the 8 vertices of the cube.
Complete step by step answer:
The geometrical representation or the structure of a face centred cubic lattice can be visually represented as follows:
As the name suggests, a Face Centred Cubic (fcc) lattice structure has atoms on all the sides of the cubic structure as well as all the vertices. There is no atom present in the centre of the cube. This brings the total count of the total number of atoms present in a Face Centred Cubic structure to 12. Considering that each vertex contains \[{\dfrac{1}{8}^{th}}\]of an atom and each face contains half an atom, the total number of atoms present in face centred cubic lattice is :
= \[\dfrac{1}{8}\](number of vertices) + \[\dfrac{1}{2}\](number of sides)
= \[\dfrac{1}{8}\](8) + \[\dfrac{1}{2}\](6)
\[ = {\text{ }}1{\text{ }} + {\text{ }}3\]
\[ = {\text{ }}4 \]atoms
Hence in FCC, there are 4 atoms per unit cell.
-In order to understand the number of neighbours around each particle in a face-centred cubic, we must understand a concept known as Coordination number.
-In chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it.
-The coordination number is fixed for a certain type of lattice structure. And for Face Centred Cubic lattice structure, the coordination number is 12.
-Hence, by definition, the number of neighbours around each particle in a face-centred cubic lattice is 12.
Hence, Option C is the correct option.
Note:
The coordination number for the various types of cubic arrangements are as follows:
Simple cubic lattice: 6
Body centred cubic lattice: 8
Face centred cubic lattice: 12
In a face centred cubic (fcc) lattice, the atoms of the given substance are located on all 6 sides of the cubic structure as well as on all the 8 vertices of the cube.
Complete step by step answer:
The geometrical representation or the structure of a face centred cubic lattice can be visually represented as follows:
![seo images](https://www.vedantu.com/question-sets/3be6149d-dc24-4676-8a7f-504e35890caf147036198372845833.png)
As the name suggests, a Face Centred Cubic (fcc) lattice structure has atoms on all the sides of the cubic structure as well as all the vertices. There is no atom present in the centre of the cube. This brings the total count of the total number of atoms present in a Face Centred Cubic structure to 12. Considering that each vertex contains \[{\dfrac{1}{8}^{th}}\]of an atom and each face contains half an atom, the total number of atoms present in face centred cubic lattice is :
= \[\dfrac{1}{8}\](number of vertices) + \[\dfrac{1}{2}\](number of sides)
= \[\dfrac{1}{8}\](8) + \[\dfrac{1}{2}\](6)
\[ = {\text{ }}1{\text{ }} + {\text{ }}3\]
\[ = {\text{ }}4 \]atoms
Hence in FCC, there are 4 atoms per unit cell.
-In order to understand the number of neighbours around each particle in a face-centred cubic, we must understand a concept known as Coordination number.
-In chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it.
-The coordination number is fixed for a certain type of lattice structure. And for Face Centred Cubic lattice structure, the coordination number is 12.
-Hence, by definition, the number of neighbours around each particle in a face-centred cubic lattice is 12.
Hence, Option C is the correct option.
Note:
The coordination number for the various types of cubic arrangements are as follows:
Simple cubic lattice: 6
Body centred cubic lattice: 8
Face centred cubic lattice: 12
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)